Robust Three-Frequency Number-Theoretical Temporal Phase Unwrapping for Phase-Differencing Profilometry.

Abstract

Achieving three-dimensional (3D) imaging with high flexibility and high robustness has long been a challenge for fringe projection profilometry (FPP). In order to address this challenge, a three-frequency number-theoretical temporal phase unwrapping (TFNT-TPU) method for phase-differencing profilometry (PDP) is proposed. By utilizing the isophase closure feature of the wrapped phase difference just caused by the measured object itself and the loose constraint relationship among the gratings with three different frequencies, 3D imaging with high flexibility can be achieved. Furthermore, to further enhance the error resistance and robustness of the proposed TFNT-TPU, an optimized design scheme for the parameters is established to suppress random errors. Additionally, a self-correction strategy is also proposed to suppress computing errors caused by arctangent operation. A series of theoretical analyses and experiments demonstrate that the 3D imaging with high flexibility and high robustness can be achieved by the proposed method.